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| HAL: hal-00342278, version 1 |
| arXiv: 0811.4714 |
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| Fast rotating Bose-Einstein condensates in an asymmetric trap |
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| Amandine Aftalion 1Xavier Blanc 2 |
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| (2008-11-27) |
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| We investigate the effect of the anisotropy of a harmonic trap on the behaviour of a fast rotating Bose-Einstein condensate. This is done in the framework of the 2D Gross-Pitaevskii equation and requires a symplectic reduction of the quadratic form defining the energy. This reduction allows us to simplify the energy on a Bargmann space and study the asymptotics of large rotational velocity. We characterize two regimes of velocity and anisotropy; in the first one where the behaviour is similar to the isotropic case, we construct an upper bound: a hexagonal Abrikosov lattice of vortices, with an inverted parabola profile. The second regime deals with very large velocities, a case in which we prove that the ground state does not display vortices in the bulk, with a 1D limiting problem. In that case, we show that the coarse grained atomic density behaves like an inverted parabola with large radius in the deconfined direction but keeps a fixed profile given by a Gaussian in the other direction. The features of this second regime appear as new phenomena. |
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| 1: | Centre de Mathématiques Appliquées (CMAP) |
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CNRS : UMR7641 – Université de Versailles Saint-Quentin-en-Yvelines – Polytechnique - X |
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| 2: | Laboratoire Jacques-Louis Lions (LJLL) |
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CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI |
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| 3: | Institut de Mathématiques de Jussieu (IMJ) |
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CNRS : UMR7586 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot |
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| Subject | : | Mathematics/Analysis of PDEs |
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| Bose-Einstein condensates – Bargmann spaces – Metaplectic transformation – Theta functions – Abrikosov lattice |
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| Attached file list to this document: | ||||||||||
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| hal-00342278, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00342278 | |
| oai:hal.archives-ouvertes.fr:hal-00342278 | |
| From: Amandine Aftalion | |
| Submitted on: Thursday, 27 November 2008 07:22:01 | |
| Updated on: Friday, 28 November 2008 14:29:45 | |
